Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
540 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator | C22×C61 | C23×C4 |
| Fitting | C2×C4×D4×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C2×C4×D4 | D61 |
| hypocenter | C61 | #2319 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16839661 | C2 | semidirect |
| 3. #16839655 | C2 | semidirect |
| 4. #16839625 | C2 | semidirect |
| 5. #16839622 | C2 | semidirect |
| 6. C4×C4⋊Dic61 | C2 | semidirect |
| 7. #16839608 | C2 | semidirect |
| 22. C4×D4×C61 | C4 | semidirect |
| 105. C61 | #2319 | semidirect |
| 108. C4×D4 | Dic61 | semidirect |